Advertisements
Advertisements
Question
Find the expression for the resistors connected in series and write the two characteristics of it. (Draw figure).
Advertisements
Solution
Expression for the resistors in series:
R1, R2 and R3 are the three resistors connected in series between points C and D as shown in the figure above. I is the current and V is the PD across points
C and D.
Rs is the effective resistance in a circuit, and V1, V2 and V3 are the potentials across the three resistors such that
V = V1 + V2 + V3 ---- (1)
Using Ohm’s law, the total potential difference
V = I Rs
and V1 = IR1, V2 = IR2 and V3 = IR3
Substituting these values in Equation 1, we get
IRs = IR1 + IR2 + IR3
∴ Rs = R1 + R2 + R3
For n number of resistors connected in series,
Rs = R1 + R2 + R3 + R4 + ----- + Rn
Characteristics of a series combination of resistors:
a) The same current flows through each resistor.
b) The effective resistance of the combination is greater than any of the resistances in the combination.
c) The effective resistance of the combination is equal to the sum of individual resistors.
APPEARS IN
RELATED QUESTIONS
In series combination which remains constant?
(a) Voltage
(b) Current
(c) Both current and voltage
(d) Both are variables
If the equivalent resistance is to be increased, then the number of resistances should be connected in
- Series
- Parallel
- Mixed arrangement
- None of the above
If the length of a wire is doubled by taking more of wire, what happens to its resistance?
Write down an expression for the resistance of a metallic wire in terms of the resistivity.
Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 27 × 10−8 Ωm.
Calculate the combined resistance in the given case:
The diagram below shows part of a circuit:
If this arrangement of three resistors was to be replaced by a single resistor, its resistance should be:
(a) 9 Ω
(b) 4 Ω
(c) 6 Ω
(d) 18 Ω
What is (a) highest, and (b)Ω lowest, resistance which can be obtained by combining four resistors having the following resistances?
4 Ω, 8 Ω, 12 Ω, 24 Ω
State the order of resistivity of (i) a metal, (ii) a semiconductor and (iii) an insulator.
A graph is plotted taking p.d. along y-axis and electric current along x-axis. Name the physical quantity that represents the slope of this graph (Fig.).
Name the material of wire used for making standard resistances. Give a reason.
What material is used for making wire to prepare heating coils? Give a reason.
How does the resistivity of a semiconductor depend on temperature?
2Ω resistor A, 1Ω resistor B and 4Ω resistor C are connected in parallel. The combination is connected across a 2V battery of negligible resistance. Draw the diagram of the arrangement and calculate:
(i) The current in each resistor A and C,
(ii) The current through battery.
Two resistors of 4Ω and 6Ω are connected in parallel to a cell to draw 0.5 A current from the cell. Calculate the current in each resistor.
What should be the length of a nickel wire of area of cross-section 3 mm2 used for making a rheostat of 750 ohm? (ρ of nickle = 0.069 Ohm mm2/m)
Two wires of the same length and area made of two materials of resistivity ρ1 and ρ2 are connected in series to a source of potential V. The equivalent resistivity for the same area is:
